Atomic force microscope for high speed imaging including integral actuator and sensor

ABSTRACT

A cantilever for a scanning probe microscope (SPM) includes a piezoelectric element in a thicker, less flexible section near the fixed base of the cantilever and a piezoresistor in a thinner, more flexible section near the free end of the cantilever. When the SPM operates in the constant force mode, the piezoelectric element is used to control the tip-sample separation. Since the resonant frequency of the piezoelectric element is substantially higher than that of conventional piezoelectric tube scanners, much higher scan rates can be achieved. When the SPM operates in the dynamic or intermittent contact mode, a superimposed AD-DC signal is applied to the piezoelectric element, and the latter is used to vibrate the cantilever as well as to control the tip-sample spacing. In another embodiment the cantilever is supported on a knife edge and vibrates at a third or higher order resonant frequency.

RELATED APPLICATIONS

This application is a continuation-in-part of application Ser. No.08/519,108, filed Aug. 25, 1995, which is a continuation-in-part ofapplication Ser. No. 08/296,340, filed Aug. 25, 1994, now abandoned,which is a continuation-in-part of application Ser. No. 08/226,784,filed Apr. 12, 1994, now U.S. Pat. No. 5,517,280, issued May 14, 1996,each of which is incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

This invention relates to scanning probe microscopes and in particularto a cantilever used in scanning probe microscopes.

BACKGROUND OF THE INVENTION

Scanning probe microscopes operate by scanning a probe over a surfacethat is to be examined, typically in a raster pattern. One type ofscanning probe microscope is an atomic force microscope, in which theprobe consists of a cantilever with a sharp tip located near its freeend. As the cantilever is scanned, the tip interacts with the surface.This in turn causes physical changes in the cantilever which aredetected and used to generate a representation of the surface, oftendown to an atomic scale. Other types of scanning probe microscopesinclude magnetic force microscopes and electric force microscopes, whichdetect phenomena other than the topography of a sample.

An atomic force microscope can operate in several modes. In the"contact" or "constant force" mode, the tip is maintained in contactwith the surface. As the tip encounters topographical features of thesurface, the cantilever is deflected or bent. These deflections aredetected, and by means of a feedback system the distance between thecantilever and the surface is controlled so as to maintain a constantforce between the tip and the surface. In the feedback system, a signalrepresentative of the deflection of the cantilever is compared against areference voltage to produce an error signal. Using the feedbackelectronics to hold the error signal to zero, an output is generatedwhich both holds the error signal to zero by changing the tip-samplespacing, and generates a representation of the surface.

In the "dynamic" or "non-contact" mode the tip is brought very close tothe surface, and the cantilever is vibrated at a frequency which isclose to its resonant frequency. As the cantilever is scanned, thedistance between the tip and the features of the surface varies. This inturn causes the gradient of the Van der Waals and other forces betweenthe tip and the surface to change. Resulting changes in the vibrationalamplitude, frequency or phase of the cantilever are detected, and againthe distance between the cantilever and the surface is controlled by afeedback system to maintain the tip-sample separation at a constant.

The "cyclical" or "intermittent" contact" mode, described in U.S. Pat.Nos. 5,266,801 and 5,308,974, is somewhat similar to the dynamic mode,but the tip is allowed to strike the surface as the cantilever vibrates.

The separation between the cantilever and the sample surface is normallycontrolled by means of a piezoelectric tube on which the sample platformis mounted. The piezoelectric tube is part of the feedback systemmentioned above. The output of the cantilever deflection detector isdelivered to an input of the piezoelectric tube via the feedbackelectronics. Variations in this signal cause the tube to expand orcontract along its axis and thereby adjust the position of the sample inrelation to the cantilever in a direction normal to the surface of thesample. Alternatively, the cantilever can be mounted on thepiezoelectric tube.

The ability of an atomic force microscope to generate images rapidlydepends on the speed at which the cantilever is scanned over the sample.Typical scan speeds are in the range of 10 to 100 μm/sec, which meansthat images take several minutes to generate. At speeds greater thanthis level, the cantilever, as it interacts with features on the samplesurface, begins to interact at frequencies that approach the resonantfrequency of the piezoelectric tube (typically between 2 and 10 kHz).When the piezoelectric tube moves into resonance, the feedback systemused to maintain a constant tip-sample force (or spacing, if themicroscope is operating in the dynamic mode) does not function properly.

By using the principles of this invention, the scan speed attainable bythe cantilever can be significantly increased.

SUMMARY OF THE INVENTION

The cantilever of this invention is for use in a scanning probemicroscope. The scanning probe microscope also includes a scanner forscanning the sample and a feedback system for controlling the separationbetween the tip and the sample.

The cantilever of this invention comprises two sections: an actuatorsection, which includes an actuator and is located relatively near thefixed base of the cantilever; and a bending section, which is associatedwith a deflection detector and is located relatively near the free end(tip) of the cantilever. The actuator controls the position of the tiprelative to the sample. The deflection detector detects the deflectionof the cantilever.

In most embodiments, the actuator section is relatively stiff and thickas compared to the bending section. As a result, the actuator sectiondoes not bend appreciably under the influence of a force on the tip.This creates an efficient coupling of any deflection of the cantileverinto the bending section. Moreover, the relatively stiff actuatorsection can bend or move the bending section with little difficulty.

In the preferred embodiment, the actuator comprises a piezoelectricelement, and the deflection detector comprises a piezoresistor which isintegral to the bending section. In other embodiments, the actuatorsection may include, for example, a capacitive plate, and the deflectiondetector may include, for example, an optical detector, aninterferometric detector or a capacitive detector.

When the microscope operates in the dynamic or intermittent contactmodes, the actuator is used to vibrate the cantilever as well as tocontrol the tip-sample separation. In the preferred embodiment, this isaccomplished by applying an oscillatory signal to one of the electrodesof the actuator while applying a DC signal that is controlled by theoutput of the deflection detector to the other electrode.

In the preferred embodiment, the cantilever is formed of silicon, andthe piezoelectric element comprises an electrode/ZnO/electrode sandwichwhich is attached to the silicon cantilever. A portion of the siliconadjacent the piezoelectric element is heavily doped with impurities andforms a conductive region which is part of the circuit which includesthe piezoresistor. In accordance with another aspect of the invention,circuitry is provided for adjusting for stress that is induced in theheavily-doped silicon as a result of the expansion and contraction ofthe piezoelectric element. Circuitry is also provided for adjusting forcurrents that are induced in the conductive region by the currentflowing through the piezoelectric element. These corrections areprovided by properly calibrated amplifiers whose respective outputs areadded into the feedback system.

Yet another aspect of this invention yields an additional technique forcorrecting for the electrical coupling between the piezoelectric elementand the piezoresistor. An AC signal having a frequency substantiallyabove the imaging bandwidth is applied to the piezoresistor, and theoutput of the piezoresistor is delivered to a lock-in amplifier, whicheffectively demodulates the AC signal and provides an outputrepresentative of the deflection of the cantilever. Any spurious signalswhich are created by the electrical coupling between the piezoelectricelement and the piezoresistor will be at frequencies which are wellbelow the AC signal and will therefore be ignored by the lock-inamplifier. Alternatively, a conductive shield layer may be used toprevent signals applied to the piezoelectric element from being coupledto the piezoresistor.

Because the resonant frequency of the piezoelectric element issignificantly greater than the resonant frequency of a typicalpiezoelectric tube, the scan speed of the cantilever may besignificantly increased.

In accordance with another aspect of the invention, a cantilever issupported on a knife edge structure and is vibrated at a higher mode ofresonance. The actuator used to vibrate the cantilever could bepiezoelectric or capacitive, for example. This arrangement facilitatesfaster scanning rates.

BRIEF DESCRIPTION OF THE DRAWING

The principles of this invention will be better understood by referenceto the following figures of the drawing, in which like referencenumerals are used to designate similar elements.

FIG. 1A illustrates a perspective view of a cantilever representative ofa first embodiment in accordance with the invention.

FIG. 1B illustrates a perspective view of a cantilever representative ofa second embodiment in accordance with the invention.

FIG. 2 illustrates a schematic block diagram of a cantilever andassociated feedback system of an atomic force microscope designed tooperate in the constant force mode.

FIG. 3A illustrates a block diagram of the Wheatstone bridge in thefeedback system of FIG. 2.

FIG. 3B illustrates a block diagram of the feedback box in the feedbacksystem of FIG. 2.

FIG. 3C illustrates a block diagram of the current-to-voltage meter inthe feedback system of FIG. 2.

FIG. 3D illustrates a block diagram of an alternative current-to-voltagemeter that can be used in the feedback system.

FIG. 3E illustrates a block diagram of the amplifier used to correct forinduced piezoresistive stress and coupling current in the feedbacksystem of FIG. 2.

FIG. 4 illustrates an arrangement including a lock-in amplifier whichcan be used to correct for capacitive coupling between piezoelectricelement and piezoresistor.

FIG. 5 illustrates a circuit diagram of the balance circuit in thearrangement shown in FIG. 4.

FIG. 6 illustrates a graph which shows the variation of the voltageacross the piezoresistor as a function of the frequency of the signalused to drive piezoelectric element.

FIGS. 7A and 7B illustrate embodiments of a cantilever in which a shieldlayer is used to prevent electrical coupling between the piezoelectricelement and the piezoresistor.

FIGS. 8A and 8B illustrate the amplitude and phase response,respectively, of a cantilever having an integral piezoelectric elementand piezoresistor.

FIG. 9A illustrates a schematic block diagram of a cantilever andassociated feedback system of an atomic force microscope designed tooperate in the dynamic or intermittent contact modes.

FIG. 9B illustrates a schematic block diagram of a dual feedback systemthat could be used in place of the feedback system shown in FIG. 9A.

FIG. 10 illustrates a graph showing the vibrational amplitude of thecantilever as a function of tip-sample distance when the cantilever isoperating in the intermittent contact mode.

FIG. 11 illustrates a graph showing the shifting of the resonantfrequency of the cantilever as the tip-sample distance varies.

FIG. 12A illustrates an embodiment of a cantilever including apiezoelectric element to be used at non-fundamental vibrationalfrequencies.

FIGS. 12B and 12C illustrate perspective and cross-sectional views,respectively, of a cantilever including a capacitive actuator to be usedat non-fundamental vibrational frequencies.

FIGS. 13A and 13B illustrate the fundamental and third resonant modes,respectively, of a vibrating cantilever.

FIG. 14 illustrates a capacitive actuator in an alternative embodimentof the invention.

FIG. 15A illustrates an optical deflection detector in an alternativeembodiment of the invention.

FIG. 15B illustrates an interferometric deflection detector in analternative embodiment of the invention.

FIG. 15C illustrates a capacitive deflection detector in an alternativeembodiment of the invention.

DESCRIPTION OF THE INVENTION

A cantilever according to one aspect of this invention includes twosections: an actuator section located relatively near the base of thecantilever and a bending section located relatively near the tip of thecantilever. FIG. 1A shows a cantilever 10 which includes a relativelythick actuator section 11 and a relatively thin bending section 12.Actuator section 11 is defined by a piezoelectric element 13, whichcomprises a zinc oxide layer 14 sandwiched between metal electrodes 15Aand 15B. Alternatively, lead zirconate titinate (PZT) could be usedinstead of zinc oxide. As is apparent from FIG. 1A, in this embodimentcantilever 10 is U-shaped, and piezoelectric element 13 is thereforesplit into two parts which are attached to the legs of the cantilever,respectively. In other embodiments, the cantilever is solid and thepiezoresistor and associated circuit elements are formed by patternedimplantations.

Cantilever 10 is preferably formed on a silicon substrate 16 andincludes a tip 17. In bending section 12, a layer of the silicon islightly-doped (e.g., at 10¹⁸ cm⁻³) to form a piezoresistive element 18.The silicon underlying piezoelectric element 13 is more heavily doped(e.g., at 10²⁰ cm⁻³) to form a conductive region 19 which adjoinspiezoresistive element 18. The circuit which includes piezoresistiveelement 18 and conductive regions 19 is fed by a pair of bias lines 19A.

As indicated in FIG. 1A, actuator section 11 has a thickness T whilebending section 12 has a thickness t. (FIG. 1A is not drawn to scale.)For example, T could be in the range 7-20 μm and t could be in the range1-5 μm. Because T is considerably larger than t, actuator section 11 issubstantially stiffer than bending section 12. In particular, assuming agiven force against tip 17, the deflection of cantilever 10 is thedouble integral of the bending moment divided by the moment of inertiaand Young's modulus. The bending moment is a function of the forceagainst tip 17, and Young's modulus is a characteristic of the material,both of which are fixed. The moment of inertia is a parameter defined bygeometry and has the form:

    ∫∫y.sup.2 dy dx

where x and y are the distances from the center of the structure inhorizontal and vertical directions, respectively.

For the rectangular geometry of cantilever 10, the moment of inertia isproportional to the thickness cubed. Therefore, assuming a constantYoung's modulus for the entire structure, a force applied against tip 17produces little bending in actuator section 11 because actuator section11 is stiffer than bending section 12 by a factor of T³ /t³.

A voltage V_(pe) is applied to the electrodes 15A and 15B ofpiezoelectric element 13. As is well-known, the zinc oxide intermediatelayer expands and contracts as V_(pe) is varied, causing actuatorsection 11 to bend. Since the base of cantilever is fixed, the bendingof actuator section 11 causes the position of the tip 17 to change in avertical direction.

With this configuration, the bending of actuator section 11 iseffectively decoupled from the bending of section 12. That is, aperpendicular force against tip 17 will cause significant bending insection 12 but will have relatively little effect in actuator section11. Conversely, the bending of actuator section 11 that is caused by theoperation of piezoelectric element 13 is able to move or bend section 12with little difficulty.

FIG. 1B illustrates a modified cantilever 20 in which the thickness t ofsection 22 is reduced to further increase the decoupling betweensections 21 and 22.

A method of fabricating a cantilever similar to cantilevers 10 and 20 isdescribed in the parent application Ser. No. 08/296,340, now abandonedwhich is incorporated herein by reference in its entirely.

As is well-known, cantilever 10 is scanned over a sample surface as tip17 detects the topological features of the surface. Typically, the tipof the cantilever faces downwards and the cantilever is thus invertedfrom the position shown in FIG. 1A.

FIG. 2 illustrates, in block form, the feedback system that is used tocontrol cantilever 10 when it is operating in the constant force mode. Asample 30 is mounted in a normal fashion on a piezoelectric tube scanner31. Tube scanner 31 moves sample 30 in a horizontal pattern, typicallyso as to cause tip 17 to trace a raster pattern on the surface of thesample. Piezoresistive element 18 is connected as part of a Wheatstonebridge 32 (see FIG. 3A). The output of Wheatstone bridge 32 is fed to asumming unit 33, where it is added to the respective outputs of aninduced stress correction unit 34 and a coupling current correction unit35, one embodiment of which is shown in FIG. 3E. The summed outputs arethen delivered to a feedback box 36 (See FIG. 3B). The output offeedback box 36 is used to generate an image of sample 30 and is alsosent as V_(pe) to piezoelectric element 13. The output of feedback box36 is also delivered to induced stress correction unit 34, and via acurrent-to-voltage meter 37 to coupling current correction unit 35.

As shown in FIG. 3A, piezoresistive element 18 is connected inWheatstone bridge 32 along with resistors R₁ and R₂ and a variableresistor R₃, which is used for adjustment purposes. Normally, theresistance of variable resistor R₃ is set to equal the resistance ofpiezoresistor 18 when the latter is in an unflexed condition. Theresistors R₁ -R₃ and piezoresistor 18 are connected in parallelconduction paths between a Vbias and ground. The common points betweenresistors R₁ and R₂ and between variable resistor R₃ and piezoresistiveelement 18 are delivered to the inputs of an amplifier A₁. As section 12of cantilever 10 bends, the resistance of piezoresistive element 18varies, and amplifier A₁ delivers an output which is representative ofthe bending of section 12.

Feedback box 36, which is illustrated in FIG. 3B, contains a summingunit 42, a gain unit 43 and an integrator 44. The inputs of summing unit42 are the signal from Wheatstone bridge 32 and a setpoint which is usedto set the desired force between the tip of the cantilever and thesample surface. In a conventional manner, the output of summing unit 42is amplified in gain unit 43 and integrated in integrator 43.

In other embodiments of this invention, feedback box 36 could employ,instead of an integral feedback, proportional feedback or differentialfeedback, or a combination thereof.

Accordingly, when cantilever 10 is operating in the contact mode, thebending of section 12 is detected in Wheatstone bridge 32 and sent viafeedback box 36 to piezoelectric element 13. Piezoelectric element 13causes actuator section 11 to bend so as to restore the desired forcebetween tip 17 and the surface of sample 30. As distinguished from manyprior art systems, the output of feedback box 36 is not sent topiezoelectric tube scanner 31 to restore the desired force between tip17 and sample 30.

As shown in FIG. 3C, current-to-voltage meter 37 includes an amplifierA₂ and a resistor R₄, the latter being connected in the series pathbetween feedback box 36 and piezoelectric element 13 and across theinput terminals of amplifier A₂. The output of amplifier A₂ is thus avoltage which represents the size of the current flowing intopiezoelectric element 13.

Units 34 and 35 are used to adjust for errors which may occur in thesystem. Considering first induced stress correction unit 34, conductiveregion 19 (FIG. 1A) is heavily doped so as to be as conductive aspossible, but in some circumstances it may retain some piezoresistiveproperties. In these cases, the bending of actuator section 11 bypiezoelectric element 13 may create a piezoresistive effect which isread by Wheatstone bridge 32 as resulting from a bending in section 12.As shown in FIG. 3E, induced stress correction unit 34 contains anamplifier A₃ having a specified gain. In many instances thepiezoresistive effect induced in region 19 is a linear function ofV_(pe). Amplifier A₃ is calibrated by varying V_(pe) while the tip 17 issuspended in mid-air. When the change in resistance of region 19 as afunction of ΔV_(pe) has been determined, amplifier A₃ is adjusted so asto compensate for this effect, i.e., the value of the parameter "a" inthe transfer function out =ax is determined (see FIG. 2). This isaccomplished by setting the gain of the amplifier itself as well asadjusting the resistance provided by potentiometer R₅. If therelationship between ΔV_(pe) and the voltage drop across bias lines 19Ais nonlinear (e.g., out=ax+bx²), a more complex amplifier may have to beused for unit 34.

Since piezoelectric element 13 acts as a capacitor, at higherfrequencies a substantial current may flow through it, and this currentmay in turn induce a current in conductive region 19 which will producea spurious output on bias lines 19A. This can occur either whencantilever 10 is used in the dynamic or intermittent contact mode, whereV_(pe) is an oscillating signal which causes the cantilever to vibrateat a frequency near resonance, or when cantilever 10 is used in theconstant force mode, where high frequencies may be generated by feedbackbox 36.

As described above, the output signal from current-to-voltage meter 37represents the current flowing into piezoelectric element 13. Couplingcurrent correction unit 35 compensates for the effect of the currentinduced in conductive region 19 as a result of the current intopiezoelectric element 13. Unit 35 is calibrated by applying a range offrequencies to piezoelectric element 13 and measuring the shifts in theoutput voltage on lines 19A as the frequency is varied. Typically, thereis no effect until the frequency reaches a certain level, and after thatpoint is reached the output voltage varies linearly with frequency.Again, a linear amplifier will often suffice, but a second or higherorder amplifier may be required if the relationship between thefrequency of V_(pe) and the spurious output on lines 19A is not linear.

When the cantilever is operating, the respective outputs of units 34 and35 are added to the output of Wheatstone bridge 32 so that the signalV_(pe) delivered to piezoelectric element 13 has been adjusted tocompensate for the induced stress and coupling current effects. If units34 and 35 are omitted from the arrangement shown in FIG. 2, the outputof Wheatstone bridge 32 is directed to the input of feedback box 36, andcurrent-to-voltage meter 37 is omitted.

FIGS. 4 and 5 illustrate an alternative arrangement which can be used tocorrect for the capacitive coupling between piezoelectric element 13 andpiezoresistor 18. FIG. 6 illustrates a graph which shows the variationof the voltage across piezoresistor 18 as a function of the frequency ofthe signal used to drive piezoelectric element 13. The data in FIG. 6were derived experimentally by applying an AC drive signal topiezoelectric element 13 with the tip of the cantilever suspended inmidair and measuring the voltage across piezoresistor 18. The verticalaxis of FIG. 6 is in units of mV per V_(ZnO), where V_(ZnO) is theamplitude of the AC signal applied to piezoelectric element 13. Sincethe tip is not in contact with a surface, the piezoresistor isunstressed (except at the resonant frequency evidenced by the spike atabout 28 kHz). If there were no capacitive coupling, the curve in FIG. 6would be a horizontal line at 0 mV/V_(ZnO).

In the arrangement shown in FIG. 4, the elements which are the same asthose shown in FIG. 2 are designated by similar numbers. In place ofWheatstone bridge 32, however, a balancing circuit 120 is connected topiezoresistor 18, and an output of balancing circuit 120 is delivered toa lock-in amplifier 121. Balancing circuit 120 and lock-in amplifier 121are driven by an oscillator 122, which in this embodiment operates at130 kHz.

FIG. 5 illustrates a circuit diagram of balance circuit 120. An outputof oscillator 122 is directed to a transformer T₁ which has a groundedcenter-tapped secondary coil and produces equal and opposite sinusoidalsignals at nodes A and A' (shown as V sin ωt and -V sin ωt).Piezoresistor 18 is connected into a bridge 123, which includes aresistor R₁₀ having a resistance equal to piezoresistor 18. ResistorsR₁₁ and R₁₂ are also balanced (in this embodiment at 3.3K). Resistor R₁₁is in series with the parallel combination of a variable resistor R₁₃and a variable capacitor C₁. Resistor R₁₂ is in series with a variableresistor R₁₄. Bridge 123 is balanced such that the voltages at nodes Band B' are both equal to zero when the cantilever is undeflected byadjusting resistors R₁₃ and R₁₄ and by adjusting capacitor C₁ to matchthe parasitic capacitance in the circuit. Nodes B and B' are connectedto the inputs of a differential amplifier A₁₀, which in this embodimenthas a gain of 500. The output of differential amplifier A₁₀, whoseamplitude represents the deflection of cantilever 10, feeds an input oflock-in amplifier 121. Lock-in amplifier 121 demodulates the output ofbalance circuit 120 and delivers the demodulated signal to feedback unit36. As shown in FIG. 4, the output of feedback unit 36 flows to theupper electrode of piezoelectric element 13.

Using the arrangement shown in FIGS. 4 and 5, any spurious signals inpiezoresistor 18 which are created by capacitive coupling betweenpiezoelectric element 13 and piezoresistor 18 will be at frequencieswhich are well below 130 kHz and will therefore be ignored by lock-inamplifier 121.

FIGS. 7A and 7B illustrate other arrangements that can be used tominimize any capacitive coupling between piezoelectric element 13 andpiezoresistor 18. In FIG. 7A, a conductive shield layer 140, preferablyof metal, has been interposed between piezoelectric element 13 andpiezoresistor 18. Shield layer 140 covers the top surface of cantilever10 and is separated from piezoelectric element 13 by an insulating layer141, which could be formed of an oxide or nitride. Shield layer 140 isgrounded. FIG. 7B illustrates a modified version in which a bottomelectrode 15C of piezoelectric element 13 extends over the top surfaceof cantilever 10. Since electrode 15C is grounded, it acts as a shieldto prevent the input signal to piezoelectric element 13 from beingelectrically coupled to piezoresistor 18.

FIGS. 8A and 8B illustrate the amplitude and phase response of acantilever having an integral piezoelectric element and piezoresistor.The cantilever had a length of 620 μm and a ZnO piezoelectric element atits base which accounted for 265 μm of the total length. Thepiezoelectric element had a thickness equal to that of the cantileverbeam (3.5 μm) and was able to deflect the cantilever up to 4 μm. Thecantilever was placed with its tip in contact with a fixed surface, andthe piezoelectric element was driven at various sinusoidal frequencies.The amplitude and phase shift of the cantilever were recorded with anadditional lock-in amplifier, which in this test was used in conjunctionwith a voltage divider arrangement rather than the preferred bridgecircuit shown in FIG. 5.

Assuming an allowable phase margin of 45°, FIGS. 8A and 8B indicate thatthe cantilever had a maximum imaging frequency (bandwidth) of about 6.4kHz. The resonance of the cantilever with its tip in contact with thesample surface was near 44 kHz. The gradual roll-off of the phase belowthe resonance frequency of the cantilever indicates that the imagingbandwidth was limited by the detection electronics rather the mechanicalresponse of the cantilever. An imaging bandwidth equal to the resonantfrequency should be attainable if the piezoresistor and lock-inamplifier are driven at a frequency much higher than resonance.

Also shown in FIGS. 8A and 8B are the amplitude and phasecharacteristics of a piezoelectric tube actuator having a length of 2inches (a commonly used size for scans of up to 100 μm). The sharp phaseshift near 550 Hz is associated with the significantly lower resonanceof the piezoelectric tube.

Using an arrangement similar to that shown in FIGS. 4 and 5, an image ofan integrated circuit was taken with a tip velocity of 1.6 mm/sec. Thesample, which contained vertical steps 1.5 μm in height, was rasterscanned over a 15 μm×15 μm area using a one-inch long piezoelectric tubewith a fast scan rate of 50 Hz. A high resolution image of 512×512pixels was obtained in about 15 seconds. By adding an interlace to theslow scan (which was ramped with a triangular wave) and changing thepixel array to 128×128, it was possible to obtain images at a rate ofseveral frames per second.

A feedback system which is particularly suitable when cantilever 10 isoperating in the dynamic or intermittent contact modes is illustrated inFIG. 9A. Electrode 15B of piezoelectric element 13 is connected to theoutput of an oscillator 40, which in this example supplies a voltagesignal with a frequency in the range of 200 KHz to 2 MHz and anamplitude ranging from 10 mV to 20 V. With cantilever 10 vibrating, theoutput of Wheatstone bridge 32 is an oscillating signal which is passedto an RMS-to-DC converter 41. To reduce mechanical coupling from theinduced zinc oxide actuation, the output of Wheatstone bridge 32 isfirst passed through a high-pass filter 32A. This added filterattenuates frequencies in the imaging bandwidth while passingfrequencies near the cantilever driving frequency. RMS-to-DC converter41 acts as an amplitude detector which delivers a DC output which isrepresentative of the root mean square of the amplitude of the signaldelivered by Wheatstone bridge 32. Other devices, such as homodynedetectors, synchronous demodulators and lock-in amplifiers, could beused in place of RMS-to-DC converter 41 as an amplifier detector.

The output of RMS-to-DC converter 41 is summed with the setpoint voltagein summing unit 42 and is passed through gain unit 43 and integrator 44to a high voltage amplifier 45. The output of amplifier 45 is deliveredto electrode 15A of piezoelectric element 13. As tip 17 encountersfeatures of sample 30, the force gradient between the tip and samplevaries, causing the vibrational amplitude of cantilever 10 to change.This change is reflected in the output of Wheatstone bridge 32 andconsequently in the DC voltage delivered by RMS-to-DC converter 41.After being summed and amplified, this altered DC signal is delivered toelectrode 15A of piezoelectric element 13, causing the cantilever tobend by an amount necessary to restore the required separation betweentip 17 and sample 30.

An important feature of this arrangement is that piezoelectric element13 is used to cause cantilever 10 to vibrate and at the same time tocontrol the tip-sample separation. This is accomplished by superimposingor summing the respective outputs of amplifier 45 and oscillator 40.(While piezoelectric element actually sees the difference between thesesignals, the effect is the same as summing because the output ofoscillator 40 is typically a sinusoidal signal. Subtracting a sinusoidalsignal from a DC signal is equivalent to adding the DC to the sinusoidalsignal phase-shifted by 180 degrees.)

Alternatively, one of the electrodes of piezoelectric element 13 couldbe grounded and the outputs of oscillator 40 and amplifier 45 could bedelivered to an external summing amplifier, with the output of summingamplifier being passed to the other electrode of the piezoelectricelement. The arrangement shown in FIG. 9A, however, avoids the need forthe external summing amplifier.

In other embodiments, piezoelectric tube 31 is used in combination withpiezoelectric element 13 to control the tip-sample separation ofcantilever 10. The dual feedback system for such an embodiment is shownin FIG. 9B. The output of RMS-to-DC converter 41 is also connected to anintegral feedback box 46 which is similar to feedback box 36, and theoutput of feedback box 46 is connected to the z-movement input ofpiezoelectric tube 31. A feedback box 47, which uses a combination ofintegral and proportional feedback, is substituted for feedback box 36.Feedback box 47 includes an additional gain unit 48 connected inparallel with gain unit 43 and integrator 44.

In the embodiment of FIG. 9B, the z-movement of piezoelectric tube 31(which also controls the x,y movement of the sample) is used incombination which z-movement of piezoelectric element 13 to provide aconstant tip-sample separation. In the preferred embodiment,piezoelectric tube 31 handles the low-frequency feedback, arising forexample from the tilt of the sample and large topographical features inthe sample, and piezoelectric element 13 handles the high frequencyfeedback which is necessary to increase the overall bandwidth of thesystem. The advantage of having piezoelectric tube 31 and piezoelectricelement 13 share the control of the tip-sample separation is that thesystem is more tolerant of sample height changes (whether from sampletilt or other factors) that fall outside the range of the piezoelectricelement 13. The overall quality of the feedback may also be improved.

FIGS. 10 and 11 illustrate changes in the behavior of cantilever 10 whenit is operating in the dynamic or intermittent contact modes. In FIG.10, the horizontal axis is the separation between the base of thecantilever and the sample in nanometers, with zero representing theseparation that exists when the tip 17 and sample are in contact and tip17 is not vibrating (negative separations thus represent conditions inwhich the cantilever is flexed). The vertical axis is the amplitude ofvibration of cantilever 10 expressed in a normalized scale from 0 to 1.When the separation is less than about -40 nm, there is essentially novibration. In the "intermittent contact" region, the vibrationalamplitude increases quite linearly with increasing separation. Beyondthe "intermittent contact" region, the sample does not interfere withthe vibration of the cantilever, and the amplitude reaches a plateau.

FIG. 11 illustrates the vibrational amplitude of cantilever 10 at twotip-sample separations as the frequency of the output of oscillator 40(FIG. 9A) is varied. Curve X₁ shows the amplitude when the tip isrelatively close to the surface, and curve X₂ shows the amplitude whenthe tip is relatively far from the surface. Assuming an output ofoscillator 40 at a frequency W_(drive), it is seen that the amplitudeincreases from Y₁ to Y₂ as the tip is moved away from the surface of thesample. Referring to FIG. 9A, the difference between amplitude Y₁ andamplitude Y₂ is reflected in the output of Wheatstone bridge 32 andconsequently the DC output of RMS-to-DC converter 41.

Correction units similar to induced stress correction unit 34 andcoupling current correction unit 35 may also be used when the cantileveris operating in a dynamic or intermittent contact mode. FIG. 12A,however, illustrates an embodiment which may avoid the need for suchcorrections. It has been disclosed that cantilevers have severalresonant modes of oscillation (see Luginbuhl et al., "PiezoelectricCantilever Beams Actuated by PCT Sole-Jel Thin Film", Transducers '95Eurosensors IX, pages 413-416). FIGS. 13A and 13B illustrate thefundamental and third resonant modes, respectively, in both of which thefree end of the cantilever experiences a maximum amplitude of vibration.(The same is true in other higher order resonant modes in which the freeend of the cantilever vibrates.) From FIG. 13B, it is apparent thatthere is a zero point approximately one-third of the distance from thetip of the cantilever.

In the embodiment of FIG. 12A, a cantilever 70 is supported by a knifeedge 71 at the location of this zero point. Cantilever 70 is vibrated bya piezoelectric element 72, which is similar to piezoelectric element 13shown in FIG. 1A. A piezoresistor 73 is formed in cantilever 70 in amanner similar to that used in forming piezoresistor 18 in cantilever 10(FIG. 1A). Bias lines 74A and 74B connect to piezoresistor 73. Becausethere is no conductive region (similar to conductive region 19 shown inFIG. 1A) adjacent the piezoelectric element 72 the induced stress andcurrent coupling problems discussed above are not incurred. In someembodiments a single piezoelectric element may be used to vibrate agroup of cantilevers.

FIGS. 12B and 12C show perspective and cross-sectional views,respectively, of an embodiment which uses a capacitive or electrostaticactuator to control the cantilever. Cantilever 80 is supported by aknife edge 81. Knife edge 81 is positioned a distance L1 from the freeend of the cantilever and a distance L2 from the base of the cantilever.A platform 82 beneath the cantilever extends from the base to the freeend of the cantilever and beyond. Two conductive regions 83 and 84 areformed under the knife edge on opposite sides of the knife edge 81. Ifthe platform 82 is formed of silicon, for example, conductive regions 83and 84 may be heavily-doped implantations.

A piezoresistor 85 is formed in cantilever 80 in the region between theknife edge 81 and the tip of the cantilever. Piezoresistor 85 issupplied with a current through bias lines 86A and 86B, and conductiveregions 83 and 84 are connected to voltage sources through lines thatare not shown in FIGS. 12B and 12C.

An electric field E1 applied to conductive region 84 will pull the tipof the cantilever downward, and an electric field E2 applied toconductive region 83 will pull the tip of the cantilever upward. Thus,with this embodiment two independent mechanisms of control forcantilever 80 are provided. For example, as shown in FIG. 12C, analternating signal could be applied to conductive region 83 at afrequency which corresponds to the second resonant mode of cantilever80, with knife edge 81 being located at the zero point (see FIG. 13B).Simultaneously, a DC signal could be applied to conductive region 84 inorder to control the sample-tip separation. In such an arrangement,piezoresistor 85 would detect the bending of cantilever in Region 1 andwould be connected through a Wheatstone bridge to a feedback systemwhich would provide a control signal for conductive region 84.

In another embodiment, an alternating signal could be applied toconductive region 84 and a DC signal could be applied to conductiveregion 83, or the cantilever could be operated in the contact mode withDC signals applied to conductive regions 83 and 84. Other variationswill be apparent to those skilled in the art.

The speed at which images can be generated has been a limitation ofscanning probe microscopy. For cantilevers operating in the contactmode, this is attributable primarily to the need to keep the frequencyof the signal generated by the cantilever below the resonant frequencyof the cantilever and the piezoelectric element that is used to controlthe tip-sample separation. The resonant frequency of a conventionalpiezoelectric tube is in the range of from 2 to 10 kHz. For a cantileveroperating in the contact mode, a bandwidth in the range of 1 kHzgenerally permits a scanning frequency of 2 to 20 Hz, depending on thesize of the scan. The typical scan rate is in the range 10 to 100μm/sec.

A piezoelectric element such as element 13 shown in FIG. 1A has asignificantly higher resonant frequency than that of a typicalpiezoelectric tube scanner. Piezoelectric tubes can have resonances downto 500 Hz depending on the size of the tube and the mass of the samplemounted on the tube, whereas a cantilever can have fundamental resonantfrequencies as high as 1 MHz. This allows scan rates on the order of 1mm/second, which is two orders of magnitude higher than the prior artnorm. Operating in the intermittent contact mode, and vibrating thecantilever in a higher resonant mode at a frequency of 250 kHz, scanrates of more than 2 mm/second have been achieved. For scan sizes of afew microns, this allows the screen to be updated at a rate of more thanonce each second, and gives an atomic force microscope a "feel" similarto that of a scanning electron microscope. Since the tip only lightlytaps the sample surface, it is not believed that tip wear will be aproblem. Using the principles of this invention, high speed imaging canbe used to map large areas of topography (up to 100×100 μm²) while, ifnecessary, lower scanning speeds can be used where high resolution isnecessary.

Using a cantilever with an integral actuator may also significantlyreduce the time required to bring the tip of the cantilever safely to aposition on or near the sample surface at the commencement of theanalysis. This engage process entails lowering the cantilever towardsthe surface with a stepper motor until the cantilever sensor(piezoresistor, optical, etc.) receives information that the tip is nearthe surface and then signals the motor to stop or change speeds. Thecantilever sensor may also signal a piezoelectric tube (on which thesample or cantilever is mounted) to quickly retract, thereby creating ashort, controlled distance between the tip and the sample.

Because the response time of a typical piezoelectric tube is quite low,the approach must be made very slowly to insure that the tip is notdamaged in a collision with the sample surface. Using an integralactuator to control the separation between the tip and the sample wouldreduce the response time from approximately 1 ms to 1 μs. This allowsthe stepper motor to lower the tip to the surface at a much more rapidrate, thereby significantly reducing the approach time. At present, theapproach times for commercial scanning probe microscopes are on theorder of a minute; using an integral actuator can reduce this time toless than a second.

While the preferred embodiment includes a piezoelectric element as theactuator and a piezoresistor as the deflection detector, otherembodiments contain alternative devices for the actuator and deflectiondetector. Several of these alternative embodiments are described below.

A capacitive plate of the kind described in parent application Ser. No.08/296,340 can be used in place of the piezoelectric element as theactuator. FIG. 14 illustrates a capacitive plate 90 which is formedadjacent a cantilever 91. Capacitive plate 90 is formed in the actuatorsection 11 and terminates before the beginning of the bending section12. An electric signal is applied between capacitive plate 90 andcantilever 91 to cause the actuator section 12 to bend or vibrate in themanner described above.

FIGS. 15A, 15B and 15C illustrate several alternative deflectiondetectors which can be used in embodiments of the invention. FIG. 15Ashows an optical detector in which a laser beam 100 is reflected off theback of cantilever 101. As cantilever 101 deflects, the reflected laserbeam strikes a position sensitive photodetector 102 at differentlocations, allowing the deflection of cantilever 100 to be measured. Thedisplacement of beam 100 at photodetector 102 is equal to the deflectionof the cantilever 101 multiplied by the ratio between the distance ofthe detector from the cantilever and the length of the cantilever. Apiezoelectric element 103 is shown in actuator section 11. The opticaldetection method is described in G. Meyer et al., Appl.Phys.Lett. 53,1045 (1988), which is incorporated herein by reference in its entirety.

FIG. 15B shows an interferometric detector 104 which includes an opticalfiber. An optical cavity is formed between the end of the fiber and theback of cantilever 101. The interference between light reflected off theback of the cantilever and light reflected at the end of the fiber isused to measure the position of the cantilever. The interferometricdetection method is described in R. Erlandsson et al.,J.Vac.Sci.Technol., A 6, 266 (1988), which is incorporated herein byreference in its entirety.

FIG. 15C shows a deflection detector in which a capacitive plate 105 isplaced parallel to the cantilever. A voltage is impressed between thecantilever and the capacitive plate, and variations in the capacitanceare measured as the cantilever deflects. The capacitive detection methodis described in T. Goddenhenrich et al., J.Vac.Sci.Technol., A 8, 383(1990). A process of fabricating a capacitive plate adjacent to acantilever is described in J. Brugger et al., MME '92, Third EuropeanWorkshop on Micromachining, Micromechanics and Microsystems. Each of theforegoing articles is incorporated herein by reference in its entirety.

With the deflection detectors illustrated in FIGS. 15A-15C, a feedbacksystem similar to the one shown in FIG. 2 would be employed, butWheatstone bridge 32 would be omitted, the output of the deflectiondetector being applied to feedback box 36. Without a piezoresistivedeflection detector, correction units 34 and 35 would not be needed.

While several embodiments according to this invention have beendescribed, it will be understood that numerous alternative embodimentswill be apparent to those skilled in the art. For example, theprinciples of this invention are applicable to any kind of scanningprobe microscope, including but not limited to magnetic and electricfield microscopes. The broad scope of this invention, as defined in thefollowing claims, is intended to cover all such embodiments.

We claim:
 1. A scanning probe microscope comprising:a cantilevercomprising an integral piezoelectric actuator and a piezoresistor; and afeedback system linking said piezoresistor and said piezoelectricactuator, said feedback system comprising a balance circuit connected tosaid piezoresistor and a lock-in amplifier connected to an output ofsaid balance circuit, said balance circuit and said lock-in amplifierbeing connected to an output of an oscillator, an output of said lock-inamplifier representing a deflection of said cantilever and being used todrive said piezoelectric actuator.
 2. The scanning probe microscope ofclaim 1 wherein said balance circuit comprises a transformer and abridge circuit, said piezoresistor being connected in said bridgecircuit.
 3. The scanning probe microscope of claim 2 wherein saidbalance circuit further includes a differential amplifier, an output ofsaid bridge circuit being connected to an input of said differentialamplifier.
 4. The scanning probe microscope of claim 1 wherein saidfeedback system further comprises a feedback box, said feedback boxbeing connected between an output of said lock-in amplifier and saidpiezoelectric element.
 5. The scanning probe microscope of claim 4wherein an output of said feedback box is connected to a first electrodeof said piezoelectric element, a second electrode of said piezoelectricelement being connected to ground.
 6. A method of analyzing the surfaceof a sample, said method comprising:providing a scanning probemicroscope, said scanning probe microscope including a cantilever and afeedback system for controlling the distance between said cantilever andsaid surface; bringing a tip of said cantilever into a position adjacentsaid surface; scanning said surface with said tip at a rate in excess of1 mm/second.
 7. The method of claim 6 wherein said step of scanningcomprises maintaining a constant force between said tip and saidsurface.
 8. The method of claim 6 wherein said step of scanningcomprises operating said scanning probe microscope in the intermittentcontact mode.
 9. The method of claim 6 wherein said step of scanningcomprises scanning said surface with said tip at a rate in excess of 2mm/second.
 10. A method of bringing a cantilever of a scanning probemicroscope into position to analyze a sample surface, said methodcomprising:incorporating an integral piezoelectric actuator and anintegral piezoresistor in the cantilever; causing said cantilever toapproach said sample surface; detecting when a tip of said scanningprobe microscope is near said sample surface; and actuating saidpiezoelectric actuator so as to retract said tip a selected distancefrom said surface.
 11. The method of claim 10 wherein the step ofcausing a cantilever to approach said sample surface is performed usinga stepper motor.
 12. The method of claim 10 wherein said step ofdetecting when said tip is near said sample surface is performed usingsaid integral piezoresistor.